권점례 Kwon Jeom-rae , 정혜윤 Jung Hye-yun , 정수용 Jung Soo-yong

DOI: JANT Vol.37(No.2) 105-134, 2023

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The purpose of this study is to explore which performance verbs are used in the achievement standards of the Korean mathematics curriculum and how to improve them. So, first, we analyzed whether there were differences in the performance verbs included in the 2015 revised mathematics curriculum achievement standards by school level. In addition, it was analyzed whether there were differences in the performance verbs included in the mathematics curriculum in Korea and foreign countries. As a result of the analysis, both the frequency and the type of performance verbs included in the achievement standards of the Korean mathematics curriculum decreased as the school level increased. Also, performative verbs such as ‘understand’ and ‘know’ were excessively used. Similar tendencies were seen in foreign mathematics curricula, but the frequency and the type of performance verbs were higher than those in Korea, and various performance verbs were used. As a result of the study, it is suggested that performance verbs included in achievement standards need to be improved to improve middle and high school mathematics classes

방정숙 Pang Jeongsuk , 곽기우 Kwak Giwoo , 김소현 Kim Sohyeon

DOI: JANT Vol.37(No.2) 135-157, 2023

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Double scale models have been introduced in elementary mathematics textbooks under the 2015 revised mathematics curriculum. However, few studies have examined in detail how students understand or utilize such models. In this study, we analyzed how 154 sixth-grade students who had learned the division of fractions from textbooks containing double scale models understood such models. The results showed that the students tended to identify the components of the model relatively well, but had difficulties exploring the unit or the meaning of the bottom number line of a model. They also had a lot of difficulties using the double scale model to complete the computation process and explain the computation principle. Based on these findings, we discuss the implications of teaching double scale models.

심영훈 Sim Yeonghoon , 김지현 Kim Jihyun , 권민성 Kwon Minsung

DOI: JANT Vol.37(No.2) 159-181, 2023

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The purpose of this study is to explore secondary mathematics teachers' perceptions on Artificial Intelligence (AI). For this purpose, we conducted three focus group interviews with 18 secondary in-service mathematics teachers and analyzed their perceptions on AI for math and math for AI. The secondary in-service mathematics teachers perceive that AI allows to implement different types of mathematics instruction but has limitations in exploring students’ mathematical thinking and having emotional interactions with students. They also perceive that AI makes it easy to develop assessment items for teachers but teachers’ interventions are needed for grading essay-type assessment items. Lastly, the secondary in-service mathematics teachers agree the rationale of adopting the subject and its needs for students, but they perceive that they are not well prepared yet to teach the subject and do not have sufficient resources for teaching the subject and assessing students’ understanding about the subject. The findings provide implications and insights for developing individualized AI learning tools for students in the secondary level, providing AI assessment tools for teachers, and offering professional development programs for teachers to increase their understanding about the subject.

김리나 Kim Rina

DOI: JANT Vol.37(No.2) 183-197, 2023

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Mathematical listening ability(MLA) refers to the capability to listen to speech languages that contain mathematical principles and concepts and understand their meanings, distinguishing it from daily life and listening in other subject classes. In this study, I investigated 834 elementary school students' MLA adapting a MLA survey items. Through the statistical analysis results of the survey, I confirmed that students' MLA had a significant correlation with gender, grade, and school location. Female students' MLA was statistically significantly higher than that of male students. MLA increased with grade and then decreased again in 6th grade. In addition, students' MLA was statistically significant differences according to the location of the school. The results of this study might be used as the basis for follow-up research and development of teaching and learning materials related to MLA.

류지민 Ryu Jimin , 박미정 Park Mijeong

DOI: JANT Vol.37(No.2) 199-212, 2023

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The purpose of this study is to find out whether there is a difference in achievement between blocked practice and interleaved practice according to the difference in domain and type of learning content in mathematics subject, and through this result, it is to confirm whether the effect of interleaved practice in mathematics learning is due to the 'Discriminative-contrast Hypothesis' or the 'Distributed-practice Hypothesis'. Although interleaved practice is more effective than blocked practice, previous studies have not shown consistent results regarding the cause. Therefore, in this study, 103 first-year middle school students were randomly assigned to blocked practice, interleaved practice, remote blocked practice, and remote interleaved practice groups had learning activities over 4 times. The results reveals that the effect of interleaved practice appeared in similar types in the same domain, but the effect of interleaved practice did not appear in different types in different domain. In addition, through this result, it was confirmed that the effect of interleaved practice was due to the 'Discriminative-contrast hypothesis' rather than the 'Distributed-practice hypothesis'. Further research topics were suggested after the issues on the research method and the findings were discussed.

강윤지 Kang Yunji

DOI: JANT Vol.37(No.2) 213-231, 2023

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The purpose of this study was to analyze and derive pedagogical implications from elementary mathematics textbooks that align with the revised 2015 curriculum. Specifically, the focus was on the chapters related to simplifying fractions, finding a common denominator, and performing addition and subtraction of Fractions with Different Denominators. The analysis revealed that the overall structure of these chapters was similar across the textbooks, but variations existed in terms of the main activities and the textbook organization. Furthermore, different textbooks employed various types and quantities of visual representations. When designing lesson directions and content, it is crucial to consider the strengths and weaknesses of each visual representation.

권오남 Kwon Oh Nam , 오세준 Oh Se Jun , 윤정은 Yoon Jungeun , 이경원 Lee Kyungwon , 신병철 Shin Byoung Chul , 정원 Jung Won

DOI: JANT Vol.37(No.2) 233-256, 2023

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This study conducted foundational research to derive ways to use ChatGPT in mathematics education by analyzing ChatGPT's responses to questions from the National Assessment of Educational Achievement (NAEA) and the College Scholastic Ability Test (CSAT). ChatGPT, a generative artificial intelligence model, has gained attention in various fields, and there is a growing demand for its use in education as the number of users rapidly increases. To the best of our knowledge, there are very few reported cases of educational studies utilizing ChatGPT. In this study, we analyzed ChatGPT 3.5 responses to questions from the three-year National Assessment of Educational Achievement and the College Scholastic Ability Test, categorizing them based on the percentage of correct answers, the accuracy of the solution process, and types of errors. The correct answer rates for ChatGPT in the National Assessment of Educational Achievement and the College Scholastic Ability Test questions were 37.1% and 15.97%, respectively. The accuracy of ChatGPT's solution process was calculated as 3.44 for the National Assessment of Educational Achievement and 2.49 for the College Scholastic Ability Test. Errors in solving math problems with ChatGPT were classified into procedural and functional errors. Procedural errors referred to mistakes in connecting expressions to the next step or in calculations, while functional errors were related to how ChatGPT recognized, judged, and outputted text. This analysis suggests that relying solely on the percentage of correct answers should not be the criterion for assessing ChatGPT's mathematical performance, but rather a combination of the accuracy of the solution process and types of errors should be considered.

윤수미 Yun Soomi , 장혜원 Chang Hyewon

DOI: JANT Vol.37(No.2) 257-276, 2023

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Mathematical modeling can be described as a series of processes in which real-world problem situations are understood, interpreted using mathematical methods, and solved based on mathematical models. The effectiveness of mathematics instruction using mathematical modeling has been demonstrated through prior research. This study aims to explore insights for mathematical modeling instruction by analyzing the metacognitive characteristics shown in the mathematical modeling cycle, according to the mathematical thinking styles of elementary math gifted students. To achieve this, a mathematical thinking style assessment was conducted with 39 elementary math gifted students from University-affiliated Science Gifted Education Center, and based on the assessment results, they were classified into visual, analytical, and mixed groups. The metacognition manifested during the process of mathematical modeling for each group was analyzed. The analysis results revealed that metacognitive elements varied depending on the phases of modeling cycle and their mathematical thinking styles. Based on these findings, didactical implications for mathematical modeling instruction were derived.

이상구 Lee Sang-gu , 남윤 Nam Yun , 이재화 Lee Jae Hwa , 김응기 Kim Eung-ki

DOI: JANT Vol.37(No.2) 277-297, 2023

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In mathematics, the concept of convolution is widely used. The convolution operation is required for understanding computer vision and deep learning in artificial intelligence. Therefore, it is vital for this concept to be explained in college mathematics education. In this paper, we present our new teaching and learning materials on convolution available for engineering mathematics. We provide the knowledge and applications on convolution with Python-based code, and introduce Convolutional Neural Network (CNN) used for image classification as an example. These materials can be utilized in class for the teaching of convolution and help students have a good understanding of the related knowledge in artificial intelligence.

박지연 Park Jiyeon , 김민경 Kim Min Kyeong

DOI: JANT Vol.37(No.2) 299-327, 2023

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In this study, we tried to find out the level of inductive reasoning ability and the aspects of visualization components shown in students in the class using exploratory software for the 'congruence and symmetry' unit in the second semester of the 5th grade of elementary school. To this end, classes using GeoGebra, one of the exploratory software, were conducted for a total of 19 students in one class of fifth graders in elementary school, and the results of the students' activities were analyzed. As a result of this study, the level of inductive reasoning ability of students remained at a similar level or developed, and it was shown that students inferred new properties of shapes using various functions of software inductively. In addition, in terms of visualization, students were able to quickly and easily draw shapes that met the conditions, and unlike the paper-and-pencil environment, using the 'measurement' and 'symmetry' functions, they transformed and manipulated complex yet precisely ongruent and symmetrical external representations. Based on these analysis results, implications for the use of exploratory software in the area of figures were derived.